
which was derived in the matrix context for the first time in [1]} and the confinement of singularities for this relation was proven in [2]}, [1]}, see also [4]}.
In 1995, Alphonse P. Magnus [5]} for the Freud weight satisfying the Pearson equation \( W^{\prime } (z) = - \big ( z^3 + 2t z \big ) \, W (z) \, \)  presented the following scalar discrete Painlevé I equation
\({\gamma _{n}\big ( \gamma _{n-1} + \gamma _{n}+ \gamma _{n+1} \big ) + 2 t \gamma _{n} = n}.\) 
